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Simplifying -4x2 = 24x + 1 Reorder the terms: -4x2 = 1 + 24x Solving -4x2 = 1 + 24x Solving for variable 'x'. Reorder the terms: -1 + -24x + -4x2 = 1 + 24x + -1 + -24x Reorder the terms: -1 + -24x + -4x2 = 1 + -1 + 24x + -24x Combine like terms: 1 + -1 = 0 -1 + -24x + -4x2 = 0 + 24x + -24x -1 + -24x + -4x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -1 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 24x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 24x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + 24x + 4x2 = 0 Solving 1 + 24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 6x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 6x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 6x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 6x + x2 = 0 + -0.25 6x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 6x + x2 = -0.25 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -0.25 + 9 Reorder the terms: 9 + 6x + x2 = -0.25 + 9 Combine like terms: -0.25 + 9 = 8.75 9 + 6x + x2 = 8.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + 3) equal to 2.958039892 and -2.958039892.Subproblem 1
x + 3 = 2.958039892 Simplifying x + 3 = 2.958039892 Reorder the terms: 3 + x = 2.958039892 Solving 3 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.958039892 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.958039892 + -3 x = 2.958039892 + -3 Combine like terms: 2.958039892 + -3 = -0.041960108 x = -0.041960108 Simplifying x = -0.041960108Subproblem 2
x + 3 = -2.958039892 Simplifying x + 3 = -2.958039892 Reorder the terms: 3 + x = -2.958039892 Solving 3 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.958039892 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.958039892 + -3 x = -2.958039892 + -3 Combine like terms: -2.958039892 + -3 = -5.958039892 x = -5.958039892 Simplifying x = -5.958039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.041960108, -5.958039892}Solution
x = {-0.041960108, -5.958039892}
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